By Topic

Embedding Long Paths in k-Ary n-Cubes with Faulty Nodes and Links

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Stewart, I.A. ; Dept. of Comput. Sci., Durham Univ., Durham ; Yonghong Xiang

Let k ges 4 be even and let n ges 2. Consider a faulty k-ary n-cube Qk n in which the number of node faults fv and the number of link faults fe are such that fv + fe les 2n-2. We prove that given any two healthy nodes s and e of Qk n, there is a path from s to e of length at least kn - 2 fv -1 (respectively, kn - 2 fv -2) if the nodes s and e have different (respectively the same) parities (the parity of a node in Qk n is the sum modulo 2 of the elements in the n-tuple over {0,1,...,k 1} representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan et al. (2007) and by Fu (2006). Furthermore, we extend known results, obtained by Kim and Park (2000), for the case when n=2.

Published in:

Parallel and Distributed Systems, IEEE Transactions on  (Volume:19 ,  Issue: 8 )